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Abstract:
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Sensitivity tests apply a range of stimulus values to experimental subjects and record binary responses; interest lies in estimating the distribution of threshold values in the subject population, where the threshold delineates response from non-response. Quantities to be estimated include location and scale parameters, and quantiles of the distribution. Application areas range from pharmaceuticals to explosives. Where testing is expensive or time-consuming, sample sizes are often small, leading to large estimate variances, or failure of maximum likelihood estimates (MLE) to exist. We discuss methods of estimating precision in such tests, problems that may arise, and potential solutions. We present an application example where explosive devices are tested for performance and safety using a sequential design method, with electrical shock as the stimulus and detonation versus non-detonation as the response. Simulated data sets are used to demonstrate how to compensate for non-existence of the MLE by using penalized maximum likelihood, and how to increase estimate precision by combining results from multiple small tests.
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